Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1058 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 451 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D37 |
| commutator, socle, cosocle | C22×C37 | C25 |
| Fitting | C37×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D37 |
| hypocenter | C37 | #3529 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14558283 | C2 | semidirect |
| 2. #14558277 | C2 | semidirect |
| 3. #14558272 | C2 | semidirect |
| 4. #14558082 | C2 | semidirect |
| 5. #14558062 | C2 | semidirect |
| 6. #14558039 | C2 | semidirect |
| 7. C37×H(3,𝔽4) | C2 | semidirect |
| 8. C2×#10596966 | C22 | semidirect |
| 10. C23×Dic37 | C22 | semidirect |
| 11. #11924534 | C22 | semidirect |
| 13. #11924529 | C22 | semidirect |
| 14. #11924528 | C22 | semidirect |
| 15. #11924524 | C22 | semidirect |
| 16. #11924520 | C22 | semidirect |
| 17. #11924518 | C22 | semidirect |
| 19. #11924513 | C22 | semidirect |
| 20. #11924512 | C22 | semidirect |
| 21. #11924509 | C22 | semidirect |
| 24. #11924505 | C22 | semidirect |
| 25. Q8×Dic37 | C22 | semidirect |
| 27. #11924496 | C22 | semidirect |
| 28. #11924492 | C22 | semidirect |
| 29. C42×D37 | C22 | semidirect |
| 100. H(3,𝔽4) | D37 | semidirect |
| 105. C37 | #3529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558283 | 2 |
| #14558277 | 2 |
| #14558272 | 2 |
| #14558082 | 2 |
| #14558062 | 2 |
| #14558039 | 2 |
| C37×H(3,𝔽4) | 2 |
| #3529 | 37 |